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Fraction Simplifier

Reduces a fraction to lowest terms by dividing by the GCD and converts it to a mixed number, a decimal and a percentage.

When to use

You have a numerator and denominator and want the reduced fraction, its mixed-number form, decimal value or percent.

Do not use when: You need to add or multiply fractions (reduce each result with this tool afterwards) or to simplify a ratio of non-integers (use ratio).

Formula

simplified = (numerator / g) / (denominator / g) with g = gcd(|numerator|, |denominator|); decimal = numerator / denominator; percent = decimal × 100

Inputs

Parameter	Type	Unit	Required	Description
`numerator`	integer		yes	Top number of the fraction (may be negative). Range: ≥ -1000000000000000, ≤ 1000000000000000
`denominator`	integer		yes	Bottom number of the fraction; must not be 0. Range: ≥ -1000000000000000, ≤ 1000000000000000

Outputs

Output	Type	Unit	Description
`simplified`	string		Lowest-terms fraction with the sign in the numerator, e.g. '3/4' (a whole number when the denominator reduces to 1).
`simplified_numerator`	integer		Numerator after reduction.
`simplified_denominator`	integer		Denominator after reduction (always positive).
`mixed_number`	string		Whole part plus proper fraction, e.g. '2 1/2'.
`decimal`	number		numerator / denominator.
`percent`	number	%	numerator / denominator × 100.
`gcd`	integer		Greatest common divisor the fraction was divided by.

Example

6/8: {"numerator":6,"denominator":8} → {"simplified":"3/4","simplified_numerator":3,"simplified_denominator":4,"mixed_number":"3/4","decimal":0.75,"percent":75,"gcd":2}

10/4: {"numerator":10,"denominator":4} → {"simplified":"5/2","mixed_number":"2 1/2","decimal":2.5,"percent":250,"gcd":2}

GET https://tttkmbb.com/api/v1/calculate/fraction-simplifier?numerator=6&denominator=8

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/fraction-simplifier (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/fraction-simplifier · Markdown: https://tttkmbb.com/math/fraction-simplifier.md · JSON definition: https://tttkmbb.com/math/fraction-simplifier.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="fraction-simplifier"
OpenAPI operationId: calculate_simplified_fraction
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Irreducible fraction (reference)
Wikipedia – Fraction (reference)
Wolfram MathWorld – Fraction (reference)

FAQ

How is a negative fraction written?

The sign is moved to the numerator: 6/−8 becomes −3/4, and the mixed form of −5/4 is '-1 1/4'.

Can I enter decimals?

No, both parts must be integers. Convert a decimal such as 0.75 to 75/100 first (or use ratio for non-integer pairs).

Related calculators

GCD and LCM Calculator — The GCD used to reduce the fraction.
Ratio Calculator — Simplify a ratio (also works with decimals).
Percentage Calculator — Percent arithmetic on the resulting value.